Temperature dependence of the quantum Hall resistance

Abstract

We report high-precision measurements of the temperature dependence of the quantum Hall resistance for two GaAs heterostructures. The Hall resistivity ${\ensuremath{\rho}}_{\mathrm{xy}}(T)$ is found to vary linearly with the minimum resistivity along the device ${\ensuremath{\rho}}_{\mathrm{xx}}^{min}(T)$ and to depend upon the sample, Hall probe set, and magnetic field direction, but to approach a sample-independent value as $T\ensuremath{\rightarrow}0$. The temperature-dependent shift of ${\ensuremath{\rho}}_{\mathrm{xy}}(T)$ from ${\ensuremath{\rho}}_{\mathrm{xy}}(0)$ can be significant even for very flat Hall steps and is inconsistent with standard mechanisms.